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Quick and easy transfer function question

by eugenius
Tags: function, transfer
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eugenius
#1
Apr4-09, 11:58 PM
P: 38
This question is more about math than anything, but it comes up in LRC frequency analysis so much that if anyone knows it, its you guys.

I am trying to find the values of a resistor, capacitor and inductor. The only knowledge I have is that the three elements are connected in series and the output voltage is taken across the capacitor. Input voltage is just V(t) no value. But it will cancel.

I do know the transfer function H(s) for the circuit. So I use voltage division, solve for V output, V input cancels, and I end up with my own expression for the transfer function. Now I need to compare them.

This is not homework, this comes up all the time in my circuits class and I never encountered a situation where I don't know anything at all except the transfer function before, until now.

Here is the known transfer function.

1/ (s^2+ sqrt(2)*s +1)

Here is the transfer function expression I came up with using the process above.

1/ (L*C*s^2+ R*C*s+1)

So pretty much 1= LC and sqrt(2) = RC

The problem is that there are a million combinations of values of L and C that will give you 1, and R and C that will give you sqrt(2).

So how the heck do I find the values of R L and C?

I tried to use the fact that both expressions have C as a common factor, but I'm not sure how. System of linear equations could work here, but also not sure how.

Anyway please help. Its probably very easy, but I'm not sure how to do it. Thank you.
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berkeman
#2
Apr5-09, 12:05 AM
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P: 41,104
Quote Quote by eugenius View Post
This question is more about math than anything, but it comes up in LRC frequency analysis so much that if anyone knows it, its you guys.

I am trying to find the values of a resistors, capacitor and inductor. The only knowledge I have is that the three elements are connected in series and the output voltage is taken across a capacitor. Input voltage is just V(t) no value.

I also know the transfer function H(s) for the circuit. So I use voltage division, solve for V output, V input cancels, and I end up with an expression for the transfer function.

This is not homework, this comes up all the time in my circuits class and I never encountered a situation where I don't know anything at all except the transfer function before, until now.

Here is the known transfer function.

1/ (s^2+ sqrt(2)*s +1)

Here is the transfer function expression I came up with using the process above.

1/ (L*C*s^2+ R*C*s+1)

So pretty much 1= LC and sqrt(2) = RC

The problem is that there are a million combinations of values of L and C that will give you 1, and R and C that will give you sqrt(2).

So how the heck do I find the values of R L and C?

I tried to use the fact that both expressions have C as a common factor, but I'm not sure how. System of linear equations could work here, but also not sure how.

Anyway please help. Its probably very easy, but I'm not sure how to do it. Thank you.
This is still coursework, so it belongs here in HH, and not in EE. Thread moved from EE to HH/Engineering.

Can you please post the question verbatim, and the relevant equations? It's a little hard to figure out how to help with what you've posted so far.

There are some problems that are under-constrained, but usually homework/coursework questions are not underconstrained.
eugenius
#3
Apr5-09, 12:12 AM
P: 38
That is the question. I wrote it up there.

You have a circuit. Series combination of resistor, inductor, capacitor, and voltage source. All you know is that the output voltage is taken across the capacitor. You also know the transfer function of the circuit which I wrote up there.

Transfer function is Output voltage / Input voltage.

Question asked. Find values of Resistance Inductance and Capacitance. RLC.


All that other information is really extra, but it might tell someone who understands circuits if I did anything wrong in getting the expression.

I'm really only basically asking this. I have this algebraic expression.



How do I solve for L R and C?

eugenius
#4
Apr5-09, 10:33 AM
P: 38
Quick and easy transfer function question

I have helped 3 people already, and yet nobody wants to help me. How nice.

All I'm really asking is. How do I compare the 2 expressions below and solve for R L C. Don't even read the rest of my post if you don't want. Its a math question.





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